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  • 标题:Streaming Algorithms for Planar Convex Hulls
  • 本地全文:下载
  • 作者:Mart{\'i}n Farach-Colton ; Meng Li ; Meng-Tsung Tsai
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2018
  • 卷号:123
  • 页码:1-13
  • DOI:10.4230/LIPIcs.ISAAC.2018.47
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:Many classical algorithms are known for computing the convex hull of a set of n point in R^2 using O(n) space. For large point sets, whose size exceeds the size of the working space, these algorithms cannot be directly used. The current best streaming algorithm for computing the convex hull is computationally expensive, because it needs to solve a set of linear programs. In this paper, we propose simpler and faster streaming and W-stream algorithms for computing the convex hull. Our streaming algorithm has small pass complexity, which is roughly a square root of the current best bound, and it is simpler in the sense that our algorithm mainly relies on computing the convex hulls of smaller point sets. Our W-stream algorithms, one of which is deterministic and the other of which is randomized, have nearly-optimal tradeoff between the pass complexity and space usage, as we established by a new unconditional lower bound.
  • 关键词:Convex Hulls; Streaming Algorithms; Lower Bounds
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